这些算法主要是解决优化问题中的难解问题。
They are mainly applied to solve difficult optimization problems.
点覆盖问题是一个重要的有实际意义的难解问题。
Point covering problem is hard to solve with great actual value.
不过，在写诗篇的时候，大卫是一个追求敬虔的人，这意味着他探讨上帝对这些难解问题的真正心意。
But as he penned the Psalms, he was a man in search of godliness, which meant he probed god's mind about difficult subjects.
在对目前已有证书状态发布方案分析的基础上，本文提出基于二次剩余难解问题的证书撤销状态发布方案。
Following the analysis of the existing certificate revocation schemes, we propose a new certificate revocation scheme based the difficulty of resolving the Quadratic Residues problem.
本文利用椭圆曲线上离散对数难解问题，提出了一种新的密钥认证方案，密钥由用户口令和秘密密钥组成。
A new key authentication scheme was proposed. This new scheme is based on the intractability of elliptic discrete logarithms. The key is combination of password and private key.
目前的数字签名和代理数字签名方案大都是基于普通离散对数难解问题上的，其安全性已经不能满足人们的需求。
At present, digital signature and proxy digital signature schemes are almost based on ordinary separate logarithm question. And the security of the schemes couldn't satisfy the request of the people.
黑白旅行商问题(BWTSP)是近年来出现的新NP -难解问题，根据图中边是否对称可以分为无向BWTSP和有向BWTSP两种。
The black and white salesman problem (BWTSP) is a new NP-hard problem, which can be divided into the undirected BWTSP and the directed BWTSP according to the symmetry of edges in graph.
这本身并不是个难解决的问题。
我认为这个问题不太难解决。
I think the problem can be got over without too much difficulty.
这些问题很难解决。
贫困问题很难解决。
这些问题太难解决了。
这些问题很难解决。请给我一些建议。
The problems are difficult to solve. Please give me some advice.
·扑灭森林大火被认为是世界上最难解决的问题之一。
Putting out forest fire is regarded as one of the most difficult problems in the world.
如处理得当，问题不难解决。
The problem will not be difficult to solve, if properly handled.
而一旦确诊后，是否用药物治疗抑郁还是个难解决的问题。
But once diagnosed, the question of whether to treat antenatal depression with drugs is a difficult one.
这些工具都很强大，但是有一些共同的问题它们都很难解决。
The tools are sophisticated, but there are a common set of problems which they handle poorly.
这是一个很难解决的问题。
二氧化碳的问题很难解决，然而，因为它主要来源于化石燃料的燃烧，这在现代生活和商业中是必不可少的。
The carbon dioxide problem is hard to fix, however, because it comes mainly from the burning of fossil fuels, which is so essential to modern life and commerce.
有时可能会出现较难解决的问题，这可能会导致资源花费更多的时间解决该问题。
Sometimes a more difficult question arises, which causes the resource to spend a far greater amount of time solving the problem.
不幸的是，我们在这样做时碰到了一些纠缠难解的问题。
许多开发人员发现约束违反是一种很难解决的类装入问题。
Many developers find constraint violations to be a difficult type of class loading problem to resolve.
丢失或者不稳定的包信息可能是最难解决的问题。
Missing or inconsistent package information is probably the most difficult problem to solve.
针对系统的性能问题常常是非常难解决的。
A performance problem with a system is often very hard to solve.
此外，本文还提供了常见连接问题的疑难解答技巧和跟踪选项。
In addition, it provided troubleshooting techniques for common connection problems and tracing options.
这是一个很难解答的问题，因为它有那么多的答案。
It's a difficult question to tackle because there's so very much to it.
但是，零售商还有一个更难解决的问题：如何确保补充的产品及时交付到仓库？
A much more difficult problem for the retailer is to assure that replenishments for the back room are delivered in time.
所幸的是，这个问题不难解决(见清单6)。
Fortunately, it's not a difficult problem (see Listing 6) to fix.
可能我们不应该立马去谴责过去的决定，但要认识到有时会产生很难解决的问题。
And perhaps we should not be so quick to condemn the decisions of the past, but recognize that sometimes there are problems for which there are no easy solutions.
可能我们不应该立马去谴责过去的决定，但要认识到有时会产生很难解决的问题。
And perhaps we should not be so quick to condemn the decisions of the past, but recognize that sometimes there are problems for which there are no easy solutions.
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